A criterion for nondensity of integral points

Abstract

We give a general criterion for Zariski degeneration of integral points in the complement of a divisor with components in a variety of dimension defined over or over a quadratic imaginary field. The key condition is that the intersection of the components of is not well approximated by rational points, and we discuss several cases where this assumption is satisfied. We also prove a greatest common divisor (GCD) bound for algebraic points in varieties, which can be of independent interest.